Accurate simulation of terrestrial ecological carbon cycles is crucial for global climate change and ecosystem management. Process-based carbon models have high interpretability, but suffer from insufficient accuracy and slow computation due to fixed parameters. In contrast, deep-learning carbon models achieve high accuracy, but disregard physical principles, which prevents ecologists from explaining ecosystem dynamics. We propose NeuroDALEC, an interpretable framework that embeds the DALEC carbon-cycle model within a neural network, enabling differentiable computation of ecological processes. Key parameters and ensemble learning strategies are designed, and mass-conserving carbon pool state transition equations are introduced to ensure physical consistency. Experiments show NeuroDALEC outperforms existing models in both accuracy and efficiency. Moreover, it provides sufficient interpretability by predicting all components of the carbon cycle. Deployed in a real-time carbon assimilation system, NeuroDALEC supports daily carbon forecasting and decision-making. This work contributes to the United Nations' Sustainable Development Goals 13 (Climate Action) and 15 (Life on Land). The source code is available at: https://github.com/codesiena/NeuroDALEC.